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Fluids
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Lattice Boltzmann Methods: Fundamentals and Applications
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Lattice Boltzmann Methods: Fundamentals and Applications

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: 30 June 2025 | Viewed by 5836

Special Issue Editor

Dr. Jie Bao

E-Mail Website
Guest Editor
Experimental and Computational Engineering Group, Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA
Interests: fluid dynamics; numerical method; electrochemistry; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Lattice Boltzamnn Method (LBM) has developed rapidly in the past 20 years. It has been utilized in various application areas, and it shows impressive advantages in different aspects, such as high efficiency for massive parallel computing, complicated geometry, and multi-phase flow. This Special Issue of Fluids is dedicated to the recent advances in the numerical approaches and applications of LBM. The studies relating to LBM include, but are not limited to, parallel computing, graphic processing unit (GPU) acceleration, new boundary condition treatments, unstructured mesh, flow for complicated geometries, multi-phase flow, multi-physics and multi-scale applications, etc.

Dr. Jie Bao
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • parallel computing
  • GPU acceleration
  • boundary condition treatments
  • unstructured mesh
  • multi-phase flow
  • multi-physics
  • multi-scale

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Published Papers (6 papers)

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Research

41 pages, 26963 KiB  
Article
Spurious Aeroacoustic Emissions in Lattice Boltzmann Simulations on Non-Uniform Grids
by Alexander Schukmann, Viktor Haas and Andreas Schneider
Fluids 2025, 10(2), 31; https://doi.org/10.3390/fluids10020031 - 28 Jan 2025
Viewed by 374
Abstract
Although there do exist a few aeroacoustic studies on harmful artificial phenomena related to the usage of non-uniform Cartesian grids in lattice Boltzmann methods (LBM), a thorough quantitative comparison between different categories of grid arrangement is still missing in the literature. In this [...] Read more.
Although there do exist a few aeroacoustic studies on harmful artificial phenomena related to the usage of non-uniform Cartesian grids in lattice Boltzmann methods (LBM), a thorough quantitative comparison between different categories of grid arrangement is still missing in the literature. In this paper, several established schemes for hierarchical grid refinement in lattice Boltzmann simulations are analyzed with respect to spurious aeroacoustic emissions using a weakly compressible model based on a D3Q19 athermal velocity set. In order to distinguish between various sources of spurious phenomena, we deploy both the classical Bhatnagar–Gross–Krook and other more recent collision models like the hybrid recursive-regularization operator, the latter of which is able to filter out detrimental non-hydrodynamic mode contributions, inherently present in the LBM dynamics. We show by means of various benchmark simulations that a cell-centered approach, either with a linear or uniform explosion procedure, as well as a vertex-centered direct-coupling method, proves to be the most suitable with regards to aeroacoustics, as they produce the least amount of spurious noise. Furthermore, it is demonstrated how simple modifications in the selection of distribution functions to be reconstructed during the communication step between fine and coarse grids affect spurious aeroacoustic artifacts in vertex-centered schemes and can thus be leveraged to positively influence stability and accuracy. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
74 pages, 7040 KiB  
Article
The Lattice Boltzmann Method with Deformable Boundary for Colonic Flow Due to Segmental Circular Contractions
by Irina Ginzburg
Fluids 2025, 10(2), 22; https://doi.org/10.3390/fluids10020022 - 21 Jan 2025
Viewed by 506
Abstract
We extend the 3D Lattice Boltzmann method with a deformable boundary (LBM-DB) for the computations of the full-volume colonic flow of the Newtonian fluid driven by the peristaltic segmented circular contractions which obey the three-step “intestinal law”: (i) deflation, (ii) inflation, and (iii) [...] Read more.
We extend the 3D Lattice Boltzmann method with a deformable boundary (LBM-DB) for the computations of the full-volume colonic flow of the Newtonian fluid driven by the peristaltic segmented circular contractions which obey the three-step “intestinal law”: (i) deflation, (ii) inflation, and (iii) elastic relaxation. The key point is that the LBM-DB accurately prescribes a curved deforming surface on the regular computational grid through precise and compact Dirichlet velocity schemes, without the need to recover for an adaptive boundary mesh or surface remesh, and without constraint of fluid volume conservation. The population “refill” of “fresh” fluid nodes, including sharp corners, is reformulated with the improved reconstruction algorithms by combining bulk and advanced boundary LBM steps with a local sub-iterative collision update. The efficient parallel LBM-DB simulations in silico then extend the physical experiments performed in vitro on the Dynamic Colon Model (DCM, 2020) to highly occlusive contractile waves. The motility scenarios are modeled both in a cylindrical tube and in a new geometry of “parabolic” transverse shape, which mimics the dynamics of realistic triangular lumen aperture. We examine the role of cross-sectional shape, motility pattern, occlusion scenario, peristaltic wave speed, elasticity effect, kinematic viscosity, inlet/outlet conditions and numerical compressibility on the temporal localization of pressure and velocity oscillations, and especially the ratio of retrograde vs antegrade velocity amplitudes, in relation to the major contractile events. The developed numerical approach could contribute to a better understanding of the intestinal physiology and pathology due to a possibility of its straightforward extension to the non-Newtonian chyme rheology and anatomical geometry. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
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12 pages, 3759 KiB  
Article
Numerical Simulation of First-Order Surface Reaction in Open Cavity Using Lattice Boltzmann Method
by Cristian Yoel Quintero-Castañeda, María Margarita Sierra-Carrillo, Arturo I. Villegas-Andrade and Javier Burgos-Vergara
Fluids 2025, 10(1), 7; https://doi.org/10.3390/fluids10010007 - 30 Dec 2024
Viewed by 497
Abstract
The lattice Boltzmann method (LBM) is a finite element and finite volume method for studying the reaction rate, mass diffusion and concentration of species. We are used the LBM to investigate the effect of the Damköhler number (Da) and Reynolds number (Re) on [...] Read more.
The lattice Boltzmann method (LBM) is a finite element and finite volume method for studying the reaction rate, mass diffusion and concentration of species. We are used the LBM to investigate the effect of the Damköhler number (Da) and Reynolds number (Re) on the laminar flow in a channel with an open square cavity and a reactive bottom wall in two dimensions in a first-order chemical reaction. The reactant A is transported through the cavity, where it undergoes a reaction on the reactive surface, resulting in the synthesis of product B. The effect of Da < 1 on the reaction rate is negligible for all investigated Re values; the generation of product B is slower because of the effect of the momentum diffusivity on the velocity inside the cavity. For Re = 5 and 1 < Da ≤ 100, the concentration of B inside the cavity reaches the maximum for Da = 100, and A is absorbed almost entirely on the bottom of the cavity. In our simulations, we observed that for all values of Re and Da > 100, the effect of the momentum diffusivity is negligible in the cavity, and the reaction on the surface is almost instantaneous. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
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62 pages, 9349 KiB  
Article
Fokker-Planck Central Moment Lattice Boltzmann Method for Effective Simulations of Fluid Dynamics
by William Schupbach and Kannan Premnath
Fluids 2024, 9(11), 255; https://doi.org/10.3390/fluids9110255 - 29 Oct 2024
Viewed by 1008
Abstract
We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation [...] Read more.
We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
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18 pages, 6740 KiB  
Article
Simulation of Corner Solidification in a Cavity Using the Lattice Boltzmann Method
by Runa Samanta and Himadri Chattopadhyay
Fluids 2024, 9(9), 195; https://doi.org/10.3390/fluids9090195 - 25 Aug 2024
Cited by 1 | Viewed by 911
Abstract
This study investigates corner solidification in a closed cavity in which the left and bottom walls are kept at a temperature lower than its initial temperature. The liquid material in the cavity initially lies at its phase transition temperature and, due to cold [...] Read more.
This study investigates corner solidification in a closed cavity in which the left and bottom walls are kept at a temperature lower than its initial temperature. The liquid material in the cavity initially lies at its phase transition temperature and, due to cold boundary conditions at the left–bottom walls, solidification starts. The simulation of corner solidification was performed using a kinetic-based lattice Boltzmann method (LBM), and the tracking of the solid–liquid interface was captured through the evaluation of time. The present investigation addresses the effect of natural convection over conduction across a wide range of higher Rayleigh numbers, from 106 to 108. The total-enthalpy-based lattice Boltzmann method (ELBM) was used to observe the thermal profiles in the entire cavity with a two-phase interface. The isotherms reveal the relative dominance of natural convection over conduction, and the pattern of interface reveals the effective growth of the solidified layer in the cavity. To quantify the uniformity of cooling, a coefficient of variation (COV) for the thermal field was calculated in the effective solidified zone at a wide range of Ra. The results show that the value of COV increases with Ra and reduces with time. The thermal instability in the flow field is also quantified through FFT analyses. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
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15 pages, 2189 KiB  
Article
Distinctions of the Emergence of Convective Flows at the “Diffusion–Convections” Boundary in Isothermal Ternary Gas Mixtures with Carbon Dioxide
by Vladimir Kossov, Dauren Zhakebayev, Olga Fedorenko and Ainur Zhumali
Fluids 2024, 9(2), 47; https://doi.org/10.3390/fluids9020047 - 12 Feb 2024
Cited by 1 | Viewed by 1684
Abstract
This study discusses the influence of the composition of a ternary gas mixture on the possibility of occurrence of convective instability under isothermal conditions due to the difference in the diffusion abilities of the components. A numerical study was carried out to study [...] Read more.
This study discusses the influence of the composition of a ternary gas mixture on the possibility of occurrence of convective instability under isothermal conditions due to the difference in the diffusion abilities of the components. A numerical study was carried out to study the change in “diffusion–concentration gravitational convection” modes in an isothermal three-component gas mixture He + CO2 − N2. The mixing process in the system under study was modeled at different initial carbon dioxide contents. To carry out a numerical experiment, a mathematical algorithm based on the D2Q9 model of lattice Boltzmann equations was used for modeling the flow of gases. We show that the model presented in the paper allows one to study the occurrence of convective structures at different heavy component contents (carbon dioxide). It has been established that in the system under study, the instability of the mechanical equilibrium occurs when the content of carbon dioxide in the mixture is more than 0.3 mole fractions. The characteristic times for the onset of convective instability and the subsequent creation of structural formations, the values of which depend on the initial content of carbon dioxide in the mixture, have been determined. Distributions of concentration, pressure and kinetic energy that allow one to specify the types of mixing and explain the occurrence of convection for a situation where, at the initial moment of time, the density of the gas mixture in the upper part of the diffusion channel is less than in the lower one, were obtained. Full article
(This article belongs to the Special Issue Lattice Boltzmann Methods: Fundamentals and Applications)
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